
It is an interpolating classifier, i.e., \({\mathcal {R}}_{\rm emp}({\rm 1{\text{-}}NN}) = 0\) .

Despite “over-fitting”,
classical analysis in [1]} shows that the classification risk of \({\cal R}({\rm 1{\text{-}}NN})\)  is (asymptotically as \(n \rightarrow \infty \) ) bounded from above by \(2{\cdot }{\mathcal {R}}(f^*)\) , where \(f^*\)  is the Bayes optimal classifier defined by Eq. REF .

Not surprisingly, given that it is an interpolating classifier, there no ERM-style analysis of 1-NN.

